The signs of radiofrequency phases and frequencies used in NMR are examined carefully. Some fundamental problems with current usage are exposed by simple examples. The entire chain of events leading to the NMR spectrum is examined closely, including generation and phase-shifting of the radiofrequency carrier wave, nuclear-spin dynamics in the presence of the radiofrequency field, quadrature detection, signal digitization, post-digitization phase shifting, Fourier transformation, and spectral presentation. Recommendations are given for software modifications which should facilitate the correspondence between pulse programming, spectral presentation, and spin dynamical theory.